Many of the phenomena that occur in nature are best characterized by random fluctuations. For example, meteorological phenomena such as fluctuations in air temperature and pressure, are characterized as random processes. The various types of sensors used to detect these processes generate random signals. As another example, thermal noise voltages generated in electronic devices generate random signals. A third example is a sonar or a radar signal, whose angle of arrival may occur at random with respect to a detection unit.
Because of the random fluctuations in such processes, the measurement and analysis techniques used for determinate signals are not suitable. Instead statistical methods are used, which are derived from a branch of statistics known as estimation theory. Essentially, it is assumed that a plausible estimate can be made from a finite number of observations.
A specific application of signal estimation is the use of distributed sensors, each associated with a processor, such that each sensor determines its own estimate of the parameter being measured. These estimates are communicated to a central unit, which determines a combined, or "fusion" estimate
Another example of signal estimation uses a single sensor, but multiple estimates are made over a period of time. The observed process is represented as a stationary signal, such as from the ambient noise in a room. The estimates are combined to obtain a combined estimate.
Distributed sensor and single sensor estimation systems are both "multi-point" systems in the sense that a number of estimates are taken for subsequent combination. For these multi-point systems, a number of methods for combining estimates have been proposed. A simple method is the use of averages. Another relatively simple method uses a least squares approach. More innovative methods include "robust methods". Each of these methods is essentially "linear" in the sense that the combined estimate is a summation of estimates multiplied by a weighting coefficient.
When random signals having more than one frequency are being detected, the methods used to measure the total signal are referred to as spectral estimation methods. Similarly, sonar or radar signals may have more than one angle of arrival. These multi-component signal estimations can be accomplished with equipment and techniques similar to that used for single component estimates, except that additional processing is required to collect and correlate, from all sensors, those estimates that are associated with each frequency or angle of arrival, before combining them. This processing involves various ranking and refitting algorithms.
Existing methods of combining estimates from multi-point systems, whether for single component or for multi-component signals, have not successfully overcome the problem of sensitivity to "bad" estimates, known as "outliers". For example, an estimate from a malfunctioning sensor that has a significant error may have a substantial adverse affect on accuracy of the combined estimate.
A need exists for a measurement system that will combine estimates with reduced sensitivity to bad estimates.